In geometry, Steffen's polyhedron is a flexible polyhedron discovered (in 1978[1]) by and named after . It is based on the Bricard octahedron, but unlike the Bricard octahedron its surface does not cross itself.[2] With nine vertices, 21 edges, and 14 triangular faces, it is the simplest possible non-crossing flexible polyhedron.[3] Its faces can be decomposed into three subsets: two six-triangle-patches from a Bricard octahedron, and two more triangles (the central two triangles of the net shown in the illustration) that link these patches together.[4]
It obeys the strong bellows conjecture, meaning that (like the Bricard octahedron on which it is based) its Dehn invariant stays constant as it flexes.[5]